Can you help me with this homework question as I cant find any formula for it. The resistance of a shunt field winding of a motor is 20 ohms at 15 degrees c. After some time of running the resistance increases to 22 ohms. Calculate the final temp of the winding given that a is 0.004 per degree celsius? Thanks.

 

Originally posted by rick@Apr 19 2005, 03:39 AM
Can you help me with this homework question as I cant find any formula for it. The resistance of a shunt field winding of a motor is 20 ohms at 15 degrees c. After some time of running the resistance increases to 22 ohms. Calculate the final temp of the winding given that a is 0.004 per degree celsius? Thanks.

[post=7061]Quoted post[/post]​

No formula. Just basic Algebra.

20 ohms = f(15)
1 Celcius = 0.004 ohms

You have 1 point and you have the slope therefor you have a line. Since you have a point and the slope, you can get the exact formula for the line and solve for any point on it.

point = (15,20)
slope = 0.004 Ohms/Celcius

so

20 Ohms = 0.004 Ohms/Celcius * 15 Celcius + Constant

From this we solve for Constant and we get 19.4 ohms

Now we have the next point we need to solve for 22 ohms,

22 Ohms = 0.004 Ohms/Celcius * X + 19.4 Ohms

X = 650 Celcius

There ya go

 

The variation of the resistance of the resistor by the temperature is gave by the formula:
R=R0[1+ α (T-T0)]
from here:
T=T0+(R/R0-1)/ α
T=15+(22/20-1)/0,004
T=40°C